QUESTION IMAGE
Question
estimating sums assignment
directions: in box a, estimate the sum by rounding to the given place value and solving. then, in box b, find the actual answer. show your work.
- 2.65 + 28.175
a. round to the nearest tenth to estimate the solution.
b. solve to find the answer.
- 3.677 + 23.14
a. round to the nearest whole number to estimate the solution.
b. solve to find the answer.
- 39.184 + 2.489
a. round to the nearest tenth to estimate the solution.
b. solve to find the answer.
math grade 5
Response
Problem 1: \(2.65 + 28.175\)
Part A: Round to the nearest tenth to estimate
Step 1: Round each number
- For \(2.65\), the hundredth digit is \(5\), so we round up the tenth digit. \(2.65\approx2.7\) (to the nearest tenth).
- For \(28.175\), the hundredth digit is \(7\), which is greater than \(5\), so we round up the tenth digit. \(28.175\approx28.2\) (to the nearest tenth).
Step 2: Add the rounded numbers
\(2.7 + 28.2 = 30.9\)
Part B: Find the actual answer
Step 1: Align the decimals and add
\[
$$\begin{align*}
&\ \ \ 2.650\\
+&28.175\\
\hline
&30.825
\end{align*}$$
\]
Problem 2: \(3.677 + 23.14\)
Part A: Round to the nearest whole number to estimate
Step 1: Round each number
- For \(3.677\), the tenth digit is \(6\), which is greater than \(5\), so we round up. \(3.677\approx4\) (to the nearest whole number).
- For \(23.14\), the tenth digit is \(1\), which is less than \(5\), so we round down. \(23.14\approx23\) (to the nearest whole number).
Step 2: Add the rounded numbers
\(4 + 23 = 27\)
Part B: Find the actual answer
Step 1: Align the decimals and add
\[
$$\begin{align*}
&\ \ \ 3.677\\
+&23.140\\
\hline
&26.817
\end{align*}$$
\]
Problem 3: \(39.184 + 2.489\)
Part A: Round to the nearest tenth to estimate
Step 1: Round each number
- For \(39.184\), the hundredth digit is \(8\), which is greater than \(5\), so we round up the tenth digit. \(39.184\approx39.2\) (to the nearest tenth).
- For \(2.489\), the hundredth digit is \(8\), which is greater than \(5\), so we round up the tenth digit. \(2.489\approx2.5\) (to the nearest tenth).
Step 2: Add the rounded numbers
\(39.2 + 2.5 = 41.7\)
Part B: Find the actual answer
Step 1: Align the decimals and add
\[
$$\begin{align*}
&\ \ 39.184\\
+&\ \ \ 2.489\\
\hline
&41.673
\end{align*}$$
\]
Final Answers
1.
- A (Estimate): \(30.9\)
- B (Actual): \(30.825\)
2.
- A (Estimate): \(27\)
- B (Actual): \(26.817\)
3.
- A (Estimate): \(41.7\)
- B (Actual): \(41.673\)
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Problem 1: \(2.65 + 28.175\)
Part A: Round to the nearest tenth to estimate
Step 1: Round each number
- For \(2.65\), the hundredth digit is \(5\), so we round up the tenth digit. \(2.65\approx2.7\) (to the nearest tenth).
- For \(28.175\), the hundredth digit is \(7\), which is greater than \(5\), so we round up the tenth digit. \(28.175\approx28.2\) (to the nearest tenth).
Step 2: Add the rounded numbers
\(2.7 + 28.2 = 30.9\)
Part B: Find the actual answer
Step 1: Align the decimals and add
\[
$$\begin{align*}
&\ \ \ 2.650\\
+&28.175\\
\hline
&30.825
\end{align*}$$
\]
Problem 2: \(3.677 + 23.14\)
Part A: Round to the nearest whole number to estimate
Step 1: Round each number
- For \(3.677\), the tenth digit is \(6\), which is greater than \(5\), so we round up. \(3.677\approx4\) (to the nearest whole number).
- For \(23.14\), the tenth digit is \(1\), which is less than \(5\), so we round down. \(23.14\approx23\) (to the nearest whole number).
Step 2: Add the rounded numbers
\(4 + 23 = 27\)
Part B: Find the actual answer
Step 1: Align the decimals and add
\[
$$\begin{align*}
&\ \ \ 3.677\\
+&23.140\\
\hline
&26.817
\end{align*}$$
\]
Problem 3: \(39.184 + 2.489\)
Part A: Round to the nearest tenth to estimate
Step 1: Round each number
- For \(39.184\), the hundredth digit is \(8\), which is greater than \(5\), so we round up the tenth digit. \(39.184\approx39.2\) (to the nearest tenth).
- For \(2.489\), the hundredth digit is \(8\), which is greater than \(5\), so we round up the tenth digit. \(2.489\approx2.5\) (to the nearest tenth).
Step 2: Add the rounded numbers
\(39.2 + 2.5 = 41.7\)
Part B: Find the actual answer
Step 1: Align the decimals and add
\[
$$\begin{align*}
&\ \ 39.184\\
+&\ \ \ 2.489\\
\hline
&41.673
\end{align*}$$
\]
Final Answers
1.
- A (Estimate): \(30.9\)
- B (Actual): \(30.825\)
2.
- A (Estimate): \(27\)
- B (Actual): \(26.817\)
3.
- A (Estimate): \(41.7\)
- B (Actual): \(41.673\)